{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sample_normal_distribution(var):\n",
    "    \"\"\"\n",
    "    Sample normal distribution with variance = var\n",
    "    \"\"\"\n",
    "    rand = np.random.uniform(low=-1.0, high=1.0, size=12)\n",
    "    return var * np.sum(rand) / 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# CONSTANT\n",
    "a = 10.\n",
    "\n",
    "# feature-based map --> list of beacons coordinate\n",
    "m = np.array([[0., 0., 0.],\n",
    "              [a, 0., 0.],\n",
    "              [a, a, a],\n",
    "              [0., a, a]])  # each row defines 1 beacon\n",
    "num_beacons = m.shape[0]\n",
    "\n",
    "var_v = 1.  # m^2/s^2\n",
    "var_z = 1.  # m^2\n",
    "\n",
    "delta_t = 0.25  # s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def motion_model(x, u):\n",
    "    \"\"\"\n",
    "    Compute motion model\n",
    "    Input:\n",
    "        x (np.ndarray) - shape 3,1 : robot location in 3D space\n",
    "        u (np.ndarray) - shape 3,1 : motion command (robot velocities)\n",
    "    Output:\n",
    "        xt (np.ndarray) - shape 3,1 : new robot location\n",
    "    \"\"\"\n",
    "    return x + u * delta_t\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def measurement_model(x, m):\n",
    "    \"\"\"\n",
    "    Compute measurement model given state x (robot loc.) & map m\n",
    "    Input:\n",
    "        x (np.ndarray) - shape 3,1 : robot location in 3D space\n",
    "        m (np.ndarray) - shape num_beacons,m : location of all beacons in the map\n",
    "    Output:\n",
    "        z (np.ndarray) - shape num_beacons, : distance from robot to each beacons\n",
    "    \"\"\"\n",
    "    return np.sqrt(np.sum((m - x.squeeze())**2, axis=1))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulation_step(x, u):\n",
    "    \"\"\"\n",
    "    Perform 1 step of simulation\n",
    "    Input:\n",
    "        x (np.ndarray) - shape (3,1) : robot location in 3D space\n",
    "        u (np.ndarray) - shape (3,1): motion command (robot velocities)\n",
    "    Output:\n",
    "        xt (np.ndarray) - shape (3,1) : new robot location\n",
    "        zt (np.ndarray) - shape (num_beacons,) : measurement at new location\n",
    "    \"\"\"\n",
    "    # Perturb motion command\n",
    "    u_noise = np.array([sample_normal_distribution(var_v) for i in range(3)])\n",
    "    u_hat = u + u_noise\n",
    "    \n",
    "    # Compute new location\n",
    "    xt = motion_model(x, u)  # here xt is the ground truth of robot location\n",
    "    \n",
    "    # Compute expected value of measurement\n",
    "    zt_bar = measurement_model(xt, m) \n",
    "    # Perturb measurement\n",
    "    zt = zt_bar + np.array([sample_normal_distribution(var_z) for i in range(num_beacons)])\n",
    "    \n",
    "    return xt, zt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ekf(muy, sigma, u, z, m):\n",
    "    \"\"\"\n",
    "    Implement an EKF to track robot location\n",
    "    Input:\n",
    "        muy (np.ndarray) - shape (3,1): expected robot location at previous time step (t-1)\n",
    "        sigma (np.ndarray) - shape (3,3): covariance of robot location at previous time step (t-1)\n",
    "        u (np.ndarray) - shape (3,1): motion command at this time step (t)\n",
    "        z (np.ndarray) - shape (num_beacons,): measurement at this time step (t)\n",
    "        m (np.ndarray) - shape (num_beacons,3): feature map contains location of all beacons\n",
    "    Output:\n",
    "        muy_t (np.ndarray) - shape (3,1): expected robot location at this time step (t)\n",
    "        sigma_t (np.ndarray) - shape (3,3): covariance of robot location at this time step (t)\n",
    "    \"\"\"\n",
    "    # predict location based on motion_model\n",
    "    muy_bar =  motion_model(muy, u)\n",
    "    # predict covariance\n",
    "    sigma_bar = sigma + delta_t * np.diag([var_v, var_v, var_v])\n",
    "    # measurement covariance\n",
    "    Q = np.array([[var_z]])\n",
    "    expected_meas = measurement_model(muy_bar, m)\n",
    "    for i in range(num_beacons):\n",
    "        # expected measurement\n",
    "        z_hat = expected_meas[i]\n",
    "        # jacobian of measurement model\n",
    "        q = np.sum((m[i, :] - muy_bar)**2)\n",
    "        x_bar, y_bar, z_bar = muy_bar.squeeze() \n",
    "        H = np.array([[x_bar - m[i, 0], y_bar - m[i, 1], z_bar - m[i, 2]]]) / np.sqrt(q)\n",
    "        # kalman update\n",
    "        S = H @ sigma_bar @ H.T + Q\n",
    "        K = sigma_bar @ H.T / S.squeeze()\n",
    "        muy_bar += K * (z[i] - z_hat)\n",
    "        sigma_bar = (np.eye(3) - K @ H) @ sigma_bar\n",
    "    \n",
    "    return muy_bar, sigma_bar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# initialize\n",
    "t = 0\n",
    "muy = np.zeros((3,1))  # initial location\n",
    "sigma = np.diag([0.1, 0.1, 0.1])  # initial covariance\n",
    "u = np.array([[0.5, 0., 0.5]]).T  # keep constant for the whole trajectory\n",
    "\n",
    "ground_truth = []\n",
    "ekf_re = []\n",
    "est_std_dev = []\n",
    "time = []\n",
    "\n",
    "# main loop\n",
    "while t < 10.:\n",
    "    # advance simulation 1 step \n",
    "    x_true, z = simulation_step(muy, u)\n",
    "    \n",
    "    # estimate new location\n",
    "    muy_bar, sigma_bar = ekf(muy, sigma, u, z, m)\n",
    "    \n",
    "    # store ground truth & estimate\n",
    "    ground_truth.append(x_true.reshape(1, -1))\n",
    "    ekf_re.append(muy_bar.reshape(1, -1))\n",
    "    est_std_dev.append(np.sqrt(np.diag(sigma_bar)))\n",
    "    time.append(t)\n",
    "    \n",
    "    # update muy & sigma\n",
    "    t += delta_t\n",
    "    muy = muy_bar\n",
    "    sigma = sigma_bar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "ground_truth = np.vstack(ground_truth)\n",
    "ekf_re = np.vstack(ekf_re)\n",
    "est_std_dev = np.vstack(est_std_dev)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0.92, '3D Trajectory')"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "ax.plot3D(ground_truth[:, 0], ground_truth[:, 1], ground_truth[:, 2], 'gray', label='truth')\n",
    "ax.scatter3D(ekf_re[:, 0], ekf_re[:, 1], ekf_re[:, 2], cmap='Greens', label='ekf')\n",
    "ax.set_xlabel('x(m)')\n",
    "ax.set_ylabel('y(m)')\n",
    "ax.set_zlabel('z(m)')\n",
    "ax.legend()\n",
    "ax.set_title('3D Trajectory')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Trajectory projected onto XZ-plane')"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ground_truth[:, 0], ground_truth[:, 2], 'r--', label='truth')\n",
    "plt.scatter(ekf_re[:, 0], ekf_re[:, 2], label='ekf')\n",
    "plt.legend()\n",
    "plt.xlabel('x(m)')\n",
    "plt.ylabel('z(m)')\n",
    "plt.title('Trajectory projected onto XZ-plane')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Estimated Standard Deviation')"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(time, est_std_dev[:, 0], label='sigma_x')\n",
    "plt.plot(time, est_std_dev[:, 1], label='sigma_y')\n",
    "plt.plot(time, est_std_dev[:, 2], label='sigma_z')\n",
    "plt.legend()\n",
    "plt.xlabel('time(sec)')\n",
    "plt.ylabel('meter')\n",
    "plt.title('Estimated Standard Deviation')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
